Trigonometry Problems

Trigonometry problems:

In this article, we shall discuss solve trigonometry problems to the students with the help of tutor. Solve trigonometry problems through the students can solve problems with step by step answers for all problems. Tutor solves trigonometry problems we need to know the basic steps involved in solving basic trigonometry problems. Solve trigonometry examples and practice problems with solution are given below.

Trigonometry Problems – Example Problems:

Example 1:

Find the value of sin-1 `(sin (3pi/5))`

Solution:

We know that sin-1 (sin x) = x.

Therefore, sin-1 (sin` (3pi/5)` ) = `(3pi)/5`

But `(3pi)/5` in` [ -pi/2, pi/2]` , which is the principal branch of sin-1 x

sin-1 (sin `(3pi/5)` )

= sin-1 (sin `(2pi/5)` ) = `(2pi)/5`

Example 2:

Show that sin-1 `3/5` – sin-1 `8/17` = cos-1 `84/85`

Solution:

Let sin-1 `3/5` = x and sin-1 `8/17` = y

Therefore sin x = `3/5` and sin y = `8/17`

Now cos x = `sqrt (1-sin^2 x)` = `sqrt(1-(9/25))` = `4/5`

and cos y = `sqrt(1-sin^2y)` = `sqrt(1-(64/289))` = `15/17`

We have cos (x – y) = cos x cos y + sin x sin y

= `4/5` x `15/17` + `3/5` x `8/17` = `84/85`

Therefore x – y = cos-1 `(84/85)`

Hence sin-1 `3/5` – sin-1 `8/17` = cos-1 `84/85`

Example 3:

Solve tan-1 2x + tan-1 3x = `pi/4`

Solution:

We have tan-1 2x + tan-1 3x = `pi/4`

(or) tan-1  `[ (2x+3x)/ (1-2x xx 3x)] ` = `pi/4`

tan-1 `[(5x)/(1-6x^2)]` = `pi/4`

Therefore `(5x)/(1-6x^2)` = tan `pi/4` = 1

(Or) 6x2 + 5x – 1 = 0

(6x – 1) (x + 1) = 0

Which gives x = `1/6` (or) x = -1

Since x = -1 does not satisfy the equation, as the LHS of the equation becomes negative, x = `1/6 ` is the only solution of the given expression.I have recently faced lot of problem while learning hard math problems with answers, But thank to online resources of math which helped me to learn myself easily on net.

Trigonometry Problems – Practice Problems:

Problem 1: tan-1 `63/16` = sin-1 `5/13` + cos-1 `33/65`

Problem 2: tan-1 `1/5` + tan-1 `1/7` + tan-1 `1/3` + tan-1 `1/8` = `pi/4`

Trigonometry problems – answer key:

Problem 1: sin-1 `5/13` + cos-1 `33/65`

Problem 2: `pi/4`